According to Marzipan in the commentary for the email marzipan (found on the strongbad_email.exe DVD), Carol is not her real guitar; her real guitar is named Joan. However, in these commentaries, Marzipan takes the rare position that the Homestar Runner characters are actors, and that the events we see in their cartoons are performed for us, and not, as everything else would imply, their actual "lives". It is debatable how literally the "Joan" comment can be taken.